Geodesic
Rational singularities and quotients by holomorphic group actions
Greb, Daniel1
1 Albert-Ludwigs-Universität Mathematisches Institut Abteilung für Reine Mathematik Eckerstr. 1 79104 Freiburg im Breisgau, Germany
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 10 (2011) no. 2, pp. 413-426

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We prove that rational and 1-rational singularities of complex spaces are stable under taking quotients by holomorphic actions of reductive and compact Lie groups. This extends a result of Boutot to the analytic category and yields a refinement of his result in the algebraic category. As one of the main technical tools vanishing theorems for cohomology groups with support on fibres of resolutions are proven.

Publié le :
Classification : 32M05, 32S05, 32C36, 14L30

Greb, Daniel 1

1 Albert-Ludwigs-Universität Mathematisches Institut Abteilung für Reine Mathematik Eckerstr. 1 79104 Freiburg im Breisgau, Germany 
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     title = {Rational singularities and quotients by holomorphic group actions},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
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     publisher = {Scuola Normale Superiore, Pisa},
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Greb, Daniel. Rational singularities and quotients by holomorphic group actions. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 10 (2011) no. 2, pp. 413-426. http://geodesic.mathdoc.fr/item/ASNSP_2011_5_10_2_413_0/